In c, is there an equivalent of "+=" for "p = p->next"?

No. You could use a macro, but i wouldn't.

If you are using C++ then instead of the raw pointers you could define your own class of iterator for a list that internally contained the pointer p.

In this case you could substitute the expression

p = p->next;

for the expression

++it;

that under the hood will do p = p->next.

Something like

iterator & operator ++()
{
    iterator::p = iterator::p->next;
    return *this;
}

where the pointer p is a data member of the class iterator.

As for the compound assignment operator then there are no such operators like ->= or .=. So you can not overload them.

According to C and C++ Standards the assignment operator is one of

= *= /= %= += -= <<= >>= &= ^= |=